Messages have been encrypted for centuries in an attempt to exchange information in perfect privacy. Some ciphering systems of the past, for example the Enigma machine of War World II fame, have approached this goal. Like other ciphering systems, however, the Enigma machine only appeared unbreakable. It was in fact broken, much to the disadvantage of Germany's war effort.
A new method of encryption, quantum cryptography, has more recently been developed. Quantum cryptography has the theoretical potential to be absolutely unbreakable. Quantum cryptography takes advantage of the Heisenberg uncertainty principle, which holds that measuring (or “observing”) a quantum system necessarily disturbs the system and yields incomplete information about the state of the system before the measurement.
Through this principle, “Alice” (a sender) and “Bob” (a receiver) may transmit through a quantum cryptographic system a cryptographic key of a random bit sequence. If the cryptographic key is undisturbed (by “Eve,” an eavesdropper) during its passage through the system, then no eavesdropping could have occurred, and the key may thereafter be used by Alice and Bob to encode and decode messages.
More specifically, in a process known as quantum key distribution (QKD), a series of photons with random polarizations may generate a sequence of numbers to create a random cryptographic key. The random cryptographic key, for example, may be used to create a one-time pad. Once securely received, the random cryptographic key may then be used to encrypt a message which can then be transmitted by any conventional means. The random cryptographic key, therefore, may allow different parties to securely communicate through email, telephone, radio or even by courier.
One way of sharing the random cryptographic key is through a well-known BB84 protocol which enables two people to jointly develop a cryptographic key from independent random choices by each person. BB84 is a four-state protocol which, as explained in “Making Unbreakable Code,” by J. Mullins, IEEE Spectrum, May 2002, pages 40-45 (incorporated herein by reference), encodes the bits of the cryptographic key in the polarization of photons. Other protocols which may be used for distributing a cryptographic key include a two-state protocol, a six-state protocol and an EPR protocol.
In BB84, Alice uses photons to send a random series of “qubits” to Bob. A “qubit” is simply a quantum two-state system, and is used to contain one unit of quantum information. In sending the qubits, Alice may encode on either a horizontal/vertical basis or a diagonal basis. When receiving the qubits, Bob randomly chooses either one of the two bases and measures each of the incoming photons. Bob and Alice then exchange their bases and keep the results of the measurements when the basis was the same. The other results of measurements may be discarded. Alice and Bob may then use the results where the bases were the same as a random cryptographic key for encryption.
Though quantum cryptography may be proved absolutely secure, practical problems may exist that can not guarantee the secrecy of the messages. For example, in virtually all experimental implementations of the BB84 protocol, the signal states are weak laser pulses rather than single photons envisaged in the original protocol. As a result, sometimes more than a single photon is sent. This may provide an opportunity for an eavesdropper to determine the key. In addition, instead of simply transmitting a key, Alice and Bob must also exchange which basis of measurement was used to determine the key. See, for example, G. Brassard, N. Lütkenhaus, T. Mor and B. C. Sanders, Phys. Rev. Lett. 85, 1330 (2000); N. Lütkenhaus, Phys. Rev. A 61, 052304 (2000); S. Felix, N. Gisin, A. Stefanov and H. Zbinden, J. Mod Optics 48, 2009 (2001); and J. Calsamiglia, S. M. Barnett and N. Lütkenhaus, quantph/0107148, all incorporated herein by reference). A legitimate user, nevertheless, may also make use of the multiple photons by improving upon the standard measurement that is used in current single photon implementations.
Implementations of the BB84 protocol in which the quantum information is encoded in the phase of the signal require a strong reference pulse to be sent along with the weak signal states to provide a phase reference. The quantum states sent may then be assumed to be coherent states, but with unknown phases, that may take one of four possible values, 0, π/2, π, 3π/2. As pointed out in M. Dusek, M. Jahma and N. Lütkenhaus, Phys. Rev. A 62, 022306 (2000) (incorporated herein by reference), if polarization is used instead of phase, the signal states are mixed states, not coherent states.
Accordingly, what is needed in the art a is way to determine the phase of a coherent state using existing quantum cryptographic systems.